A man took 4 1/2 hours to drive 360 km from Singapore to Kuala Lumpur. He used 37. 5 litres of petrol for journey. A. He drove at an average speed of 110 km / hr on a highway for 2 hours during his journey. Find his average speed for the remaining part of his journey

Answer:

19?

Step-by-step explanation:

Answer:

5000 dollars

Step-by-step explanation:

Let his budget be x

16% of x is 800 dollars

.16 * x = 800

Divide each side by .16

.16x/.16 = 800/.16

x=5000

His budget is 5000 dollars

1/12    is the probability that the sum of the two faces adds to 5 .

What does the math term "probability" mean?

The simple definition of probability is the likelihood that something will occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out.

                             Statistics describes the examination of events subject to probability.

It is because there are total of 3 pairs possible where addition of number face adds to 4.

The pairs are (2,2), (1,3), (3,1).

The total outcomes possible(sample space) is 36.

Hence probability is 3/36, that is, 1/12

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Answer:

79/120

Step-by-step explanation:

Answer:

79/120

Step-by-step explanation:

You make all the answers to have the same denomination and then add them.

The researchers are 95% confident that the difference between the two population proportions is between 0.228 and 0.47.

Regarding the second part of the question, if we assume that the two sample proportions are independent and randomly sampled from their respective populations, we can use the following formula to construct a confidence interval for the difference between population proportions (P1 - P2):

(P1 - P2) ± zsqrt((P1(1-P1)/n1) + (P2*(1-P2)/n2))

where:

P1 and P2 are the sample proportions

n1 and n2 are the sample sizes

z is the critical value from the standard normal distribution corresponding to the desired level of confidence

Assuming that Dg = 555 represents the degrees of freedom for the two sample proportions, we can find the critical value z for a 96% confidence level using a standard normal distribution table or calculator:

z = 1.7507

Since the researchers are 95% confident, we can construct a 95% confidence interval by using this value of z and plugging in the sample proportions, sample sizes, and degrees of freedom:

(P1 - P2) ± zsqrt((P1(1-P1)/n1) + (P2*(1-P2)/n2))

= (538/398) - 1 ± 1.7507sqrt((538/398)(1-(538/398))/398 + (1/555)*(1-1/555)*538/398)

= 0.352 ± 0.124

Therefore, the researchers are 95% confident that the difference between the two population proportions is between 0.228 and 0.476.

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The new coordinates are M'(-1, -7), N'(-8, -5), O'(-4, -2), and P'(3, -4)

A 180 degrees rotation denoted by R(180, 0) is a rotation that has the same effect as the 180 degrees counterclockwise of a figure.

And it has the algebraic rule of its rotation to be changed from (x, y) to (-x, -y) i.e  (x, y) ⇒ (-x, -y)

The coordinates of the parallelogram are given as

M(1, 7), N(8, 5), O(4, 2), and P(-3, 4)

The rotation is given as 180° rotation

As mentioned above,

We have (x, y) ⇒ (-x, -y)

Substitute M(1, 7), N(8, 5), O(4, 2), and P(-3, 4) in (x, y) ⇒ (-x, -y)

So, we have

M'(-1, -7), N'(-8, -5), O'(-4, -2), and P'(3, -4)

Hence, the coordinates of the image are M'(-1, -7), N'(-8, -5), O'(-4, -2), and P'(3, -4)

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The actual speed of the red car along the road is 95 feet per second.

In this scenario, the police car and the red car are located at different positions relative to the road. The police car is situated 40 feet to the side of the road, while the red car is driving along the road, 130 feet up the road from the police car.

Given that the distance between the police car and the red car is decreasing at a rate of 95 feet per second, this represents the rate at which the two cars are getting closer to each other. This rate of change is known as the "rate of decrease" or "rate of approach."

Since the red car is moving along the road, the rate at which it is traveling can be determined by considering its motion parallel to the road. In this case, the rate of approach between the two cars represents the rate at which the red car is actually traveling along the road. Therefore, the actual speed of the red car along the road is 95 feet per second.

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Answer:

n - 8  = 20

Step-by-step explanation:

Answer:

6,372.08 =

6,000

+ 300

+ 70

+ 2

+ 0.0

+ 0.08

Answer:

True :)

Please mark me brainliest!

Answer:

- (27n^3 - 12n - 1) over 3n

Step-by-step explanation:

The estimated δf for f(x) = 112 * x^2 when a = 2 and δx = -1/2 is approximately -224.

To estimate δf using linear approximation, we will use the formula: δf ≈ f'(a) * δx
Here, f(x) = 112 * x^2, a = 2, and δx = -1/2. First, we need to find the derivative of f(x) with respect to x: f'(x) = d(112 * x^2) / dx = 224 * x

Now, we will find the derivative at the point a: f'(a) = f'(2) = 224 * 2 = 448
Finally, we'll use the linear approximation formula to estimate δf: δf ≈ f'(a) * δx = 448 * (-1/2) = -224

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Answer:

i don't know maybe D. 2 and 3

The total income and expenditure of Agri-small business limited in September is R 299596 and expenditure is R 193236.

Given that the expenses on petrol be R4850.00 at the end of September, balance is R 106360.00, usage on income of salaries be 25%, on electricity,rates and taxes be 11%, 42% of the remaining on insurance and investments.

We are required to find the total income and expenditure in September.

Generally the equation for insurance is mathematically given as :

Insurance=42% of the balance

Insurance=0.42*0.64A

Insurance=0.2688A.

Generally the equation for the total after all the other expenditures is mathematically given as:

Total expenditure after all other expenditures=0.64A-0.2688A

Total expenditures after all other expenditures=0.3712A.

Total expenditures after all other expenditures is as 111210 (106360+4850)

Equating both the equation and value:

111210=3712A

A=299596

The total income is 299596.

Therefore the calculation of expense is given as:

Expense=0.25A+0.11A+0.2688A+4850

Expense=0.6288A+4850

=0.6288*299596+4850

=193236

The expense is 193236.

Hence the total income and expenditure in September are "Income is R 299596 and expenditure is R 193236.

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The total income and expenditure of Agri-small business limited in September is R 299596 and expenditure is R 193236.

We have to find the total income and expenditure in September.

The equation for insurance is mathematically given as :

Insurance = 42% of the balance

Insurance=0.42*0.64A

Insurance=0.2688A.

Total expenditure after all other expenditures = 0.64A-0.2688A

Total expenditures after all other expenditures = 0.3712A.

Total expenditures after all other expenditures is as 111210 (106360 +4850)

Equating both the equation and value:

111210 = 3712 A

A = 299596

Thus The total income is 299596.

Therefore the calculation of expense is given as:

Expense=0.25A+0.11A+0.2688A+4850

Expense=0.6288A+4850

=0.6288*299596+4850

=193236

The expense is 193236.

Hence, the total income and expenditure in September are "Income is R 299596 and expenditure is R 193236.

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Answer:

3x² + 2x - 6+(x² - 4x + 10)

3x² + 2x - 6+x²-4x+10

3x²+x²+2x-4x-6+10

4x²-2x+4

The Normal model is a good approximation for the sampling distribution.

a) According to the Central Limit Theorem, the theoretical mean and standard deviation for a sample size of 20 should be 0.05 and 0.02, respectively. For a sample size of 100, the theoretical mean and standard deviation should be 0.05 and 0.01, respectively.

b) The observed mean and standard deviation for a sample size of 20 was 0.052 and 0.021, respectively. For a sample size of 100, the observed mean and standard deviation was 0.051 and 0.012, respectively. These values are fairly close to the theoretical values.

c) Looking at the histograms in Exercise 1, I would be comfortable using the Normal model as an approximation for the sampling distribution at a sample size of 100.

d) The Success/Failure Condition states that the sample size should be large enough for the sampling distribution of the sample proportions to be approximately normal. Since I chose a sample size of 100, which satisfied the condition, I can be confident that the Normal model is a good approximation for the sampling distribution.

The sample size of 100 is large enough for the sampling distribution of the sample proportions to be approximately normal, and the observed mean and standard deviation is close to the theoretical values. Therefore, the Normal model is a good approximation for the sampling distribution.

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Answer:

54.6%

Step-by-step explanation:

The percentage change would be (36000-16000)/36000 *100% = 0.546 * 100% = 54.6%

Hope this helped!

A higher slope indicates a stronger relationship between the variables, and the sign (positive or negative) indicates the direction of the relationship (positive: both variables increase together, negative: one variable increases while the other decreases).

When comparing the slopes of the regression lines for two models, you're essentially looking at the differences in their unstandardized coefficients. These coefficients represent the change in the dependent variable for each unit change in the independent variable, keeping all other variables constant.

In the unstandardized model you mentioned, the slope of 0.96 means that for every one-unit increase in the independent variable, the dependent variable is expected to increase by 0.96 units, on average. This helps us understand the strength and direction of the relationship between the two variables in the model.

To compare the slopes between two models, simply examine their unstandardized coefficients.

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To determine whether the assumption of constant error variance is satisfied for a model with tut, independent variables x, and x₂, you would examine the residual plot where the residuals are plotted against predicted values y.

This plot is also known as the plot of residuals versus fitted values. In this plot, if the residuals are randomly scattered around the horizontal line of zero, then the assumption of constant error variance is satisfied. However, if there is a pattern in the residuals, such as a funnel shape or a curve, then the assumption of constant error variance may not be met. It is important to ensure that the assumption of constant error variance is met, as violation of this assumption can lead to biased and inefficient estimates of the model parameters. Additionally, it can affect the reliability of statistical inferences and lead to incorrect conclusions.
In summary, to determine whether the assumption of constant error variance is satisfied for a model with tut, independent variables x, and x₂, you would examine the residual plot where the residuals are plotted against predicted values y. It is important to check this assumption to ensure the validity of the model and the accuracy of the results.This plot allows you to assess the variance of the residuals and identify any patterns, which could indicate that the assumption of constant error variance may not be met. If the plot shows no discernible pattern and the spread of residuals appears to be uniform across the range of predicted values, the assumption of constant error variance is likely satisfied.

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Answer:

b) f(x) = x² - 256

Step-by-step explanation:

Since we have been given the zeros of a function, -16 and 16. We are asked to find which function truly has those zeros.

To find this, we can substitute the zeros for x in the functions to find the one that is true/correct.

A) f(x) = x² - 16

 ⇒  0 = 16² - 16          and          ⇒  0 = (-16)² - 16

 ⇒  0 = 256 - 16        and          ⇒  0 = 256 - 16

 ⇒  0 = 240 ✘          and          ⇒  0 = 240 ✘

B) f(x) = x² - 256

 ⇒  0 = 16² - 256          and          ⇒  0 = (-16)² - 256

 ⇒  0 = 256 - 256        and          ⇒  0 = 256 - 256

 ⇒  0 = 0 ✔                  and          ⇒  0 = 0 ✔

C) f(x) = x² - 32x + 256

 ⇒  0 = 16² - 32(16) + 256         and        ⇒  0 = (-16)² - 32(-16) + 256

 ⇒  0 = 256 - 512 + 256           and        ⇒  0 = 256 + 512 + 256

 ⇒  0 = 512 - 512                       and        ⇒  0 = 512 + 512

 ⇒  0 = 0 ✔                               and        ⇒  0 = 1,024 ✘

D) f(x) = x² + 32x + 256

  ⇒  0 = 16² + 32(16) + 256         and        ⇒  0 = (-16)² + 32(-16) + 256

  ⇒  0 = 256 + 512 + 256           and         ⇒  0 = 256 - 512 + 256

  ⇒  0 = 512 + 512                       and         ⇒  0 = 512 - 512

  ⇒  0 = 1,024 ✘                          and        ⇒  0 = 0 ✔

Therefore, Function B has the zeros of x = -16 and x = 16.

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Answer:  \(\bold{y=-\dfrac{1}{3}x+6}\)

                \(\bold{y=-\dfrac{1}{4}x+\dfrac{25}{4}}\)

Step-by-step explanation:

  x + 3y = 18

- x           -x

        3y = -x + 18

      ÷3     ÷3 ÷3

         y = (-1/3)x + 6

-3x - 12y = -75

+3x           +3x

        -12y = 3x - 75

       ÷-12    ÷-12 ÷-12

           y = (-1/4)x + (25/4)

From the use of the angle of elevation, the length of ladder is 47 feet.

The angle between the horizontal and a line of sight or an object above the horizontal, which is commonly stated in degrees or radians, is known as the angle of elevation. Determining an object's position in relation to an observer or a reference point is a common use of trigonometry and geometry.

We know that we have to use the idea of the angle of elevation in this case. We know that;

Cos 65 = 20/x

x is the length of the ladder

x =20/Cos 65

x = 20/0.4225

x = 47 feet

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|AC|^2 = |AB|^2 + |BC|^2  is indeed the Pythagorean theorem which implies that adding the hypotenuse square as well as the two sides of a right triangle equals the hypotenuse square.

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

|AC|^2 = |AB|^2 + |BC|^2    

where |AB| = length of line segment AB. (AB and BC are the rest of the two sides of that triangle ABC, AC being the hypotenuse).

Calculating value by using the Pythagorean theorem:

The smallest side of the triangle in this instance contains 2 dots, which equals.

The triangle's bigger side has 3 dots.

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Answer: 3.75 miles

Step-by-step explanation:

Divide 30 by 8. 30/8= 3.75. If she walked 1/8 then she walked 3.75 miles

1st graph.

It shows the accurate descent and rise as well as the constant motion.

Answer:

The answer is the top-left graph.

Step-by-step explanation:

The most likely next step is 2x = -25.To find the most likely next step, let's analyze the given equations:

Step 1: 6x + 10 - 4x = -4 - 11

Step 2: 6x + 10 - 4x = -15

Step 3: 2x + 10 = -15

In Step 2, the equation simplifies by combining like terms on both sides of the equation, resulting in -15 on the right side.

To proceed, we need to isolate the variable x. In this case, we can continue by subtracting 10 from both sides of the equation:

Step 4: 2x = -15 - 10

Simplifying further:

Step 4: 2x = -25

Therefore, the most likely next step is 2x = -25.

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Answer:

The type of number that represents -4/2 is:

Choice B) Integer

Choice C) Rational

Step-by-step explanation:

The number -4/2 is an integer because it represents a whole number (-2) and it is also a rational number because it can be expressed as a fraction of two integers.

-4/2 is an :

Solution:

Before we make any decisions about the type of number -4/2 is, let's simplify it first.

It's the same as -2. Now, let's familiarize ourselves with the sets of numbers out there. Where does -2 fit in?

______________

This set incorporates only positive numbers and zero. So -2 doesn't belong here.

This set incorporates whole numbers and negative numbers. So -2 belongs here.

This set has integers, fractions, and decimals. So -2 does belong here too.

This is a set for numbers that cannot be written in fraction form (a/b, where b ≠ 0). So -2 doesn't belong here.

-4/2 belongs in the integer and rationals set.